Hidden symmetry of flexoelectric coupling

Abstract

Considering the importance of the flexoelectric coupling for the physical understanding of the gradient-driven couplings in mesoscale and nanoscale solids, one has to determine its full symmetry and numerical values. The totality of available experimental and theoretical information about the flexocoupling tensor symmetry (specifically the amount of measurable independent components) and numerical values is contradictory. However, the discrepancy between the theory and experiment can be eliminated by consideration all possible inner symmetries of the flexocoupling tensor and physical limits on it components values. Specifically, this study reveals the inner "hidden" symmetry of the static flexoelectric tensor that allows minimizing the number of its independent components. Revealed hidden symmetry leads to nontrivial physical sequences, namely it affects on the upper limits of the static flexocoupling constants. Also we analyze the dynamic flexoelectric coupling symmetry and established the upper limits for the numerical values of its components. These results can help to understand and quantify the fundamentals of the gradient-type couplings in different solids.

Size effect of soft phonon dispersion in nanosized ferroics

“…corresponding to cubic m3m paraelectric (see, e.g., Table I for SrTiO 3 ) allowing for the hidden permutation symmetry of the static flexocoupling [37]. For the case the inverse static dielectric susceptibility (16) tends to zero at ( )…”

“…The static flexoelectric effect, firstly introduced by Mashkevich, Tolpygo [29], and Kogan [30], manifesting itself in the appearance of electric polarization variation linearly proportional to the strain gradient Considering the importance of the flexoelectric coupling (shortly "flexocoupling") for the physical understanding of the gradient-driven couplings in mesoscale and nanoscale solids, one has to determine its symmetry and numerical values. Unfortunately, the available experimental and theoretical data about the flexocoupling tensor symmetry, specifically the amount of independent components allowing for the point group symmetry [35,36] and "hidden" permutation symmetry [37], and numerical values are contradictory [38]. Namely, the upper limits for the values ijkl f established by Yudin et al [39], as well as the values calculated from the first principles for bulk ferroics [40,41,42,43,44], the can be several orders of magnitude smaller than those measured experimentally in ferroelectric ceramics [45,46,47] and thin films [48], ferroelectric relaxor polymers [49] and electrets [50], incipient ferroelectrics [51,52] and biological membranes [53,54].…”